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Are Price-Earnings Ratios Mean Reverting? an Empirical Study Kevin Klassen Gettysburg College Class of 2019

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Are Price-Earnings Ratios Mean Reverting? an Empirical Study Kevin Klassen Gettysburg College Class of 2019 Volume 11 Article 3 2019 Are Price-Earnings Ratios Mean Reverting? An Empirical Study Kevin Klassen Gettysburg College Class of 2019 Follow this and additional works at: https://cupola.gettysburg.edu/ger Part of the Finance Commons, and the Growth and Development Commons Share feedback about the accessibility of this item. Klassen, Kevin (2019) "Are Price-Earnings Ratios Mean Reverting? An Empirical Study," Gettysburg Economic Review: Vol. 11 , Article 3. Available at: https://cupola.gettysburg.edu/ger/vol11/iss1/3 This open access article is brought to you by The uC pola: Scholarship at Gettysburg College. It has been accepted for inclusion by an authorized administrator of The uC pola. For more information, please contact [email protected]. Are Price-Earnings Ratios Mean Reverting? An Empirical Study Abstract Mean reversion in stock prices is a highly studied area in the financial literature with controversial findings. While some economists have found evidence of mean reverting processes in stock prices, many argue in favor of the Efficient Market Hypothesis which states stock prices are random walk processes. This paper seeks to add to the literature on mean reversion but testing for evidence in price-earnings ratios rather than stock prices. The tudys employs a robust regression model controlling for company-specific nda general market factors that influence price-earnings ratio deviations. After correcting for heteroskedasticity, serial correlation, and unit root processes, the results indicate mean reverting behavior does exist in US equities from 2008- 2017 and mean reversion in price-earnings ratios may occur more quickly than mean reversion of stock prices. The outcome of this paper also implies some level of endogeneity in the Three-Factor-Model proposed by Fama and French (1992). Keywords mean reversion, stock market, Efficient Market Hypothesis, regression model, Three-Factor-Model This article is available in Gettysburg Economic Review: https://cupola.gettysburg.edu/ger/vol11/iss1/3 Are Price-Earnings Ratios Mean Reverting? An Empirical Study Kevin Klassen Gettysburg College [email protected] April 2019 Abstract Mean reversion in stock prices is a highly studied area in the financial literature with controversial findings. While some economists have found evidence of mean reverting processes in stock prices, many argue in favor of the Efficient Market Hypothesis which states stock prices are random walk processes. This paper seeks to add to the literature on mean reversion but testing for evidence in price-earnings ratios rather than stock prices. The study employs a robust regression model controlling for company-specific and general market factors that influence price-earnings ratio deviations. After correcting for heteroskedasticity, serial correlation, and unit root processes, the results indicate mean reverting behavior does exist in US equities from 2008- 2017 and mean reversion in price-earnings ratios may occur more quickly than mean reversion of stock prices. The outcome of this paper also implies some level of endogeneity in the Three- Factor-Model proposed by Fama and French (1992). Acknowledgements: I would like to thank Professor Cadigan, Professor Murphy, Professor Cushing-Daniels, Professor Weise, Professor O’Brien, Polina Rozhkova, and Luca Menicali for helpful suggestions in my topic selection, data organization, empirical analysis and paper structure. 4 I. Introduction Whether stock prices and ratios can be described as random walk or mean reverting processes is highly controversial within the financial literature. Mean reversion refers to a tendency of asset prices or ratios to return to a trend path. This paper sets out to examine whether the price-earnings (P/E) ratios of US companies have transitory components and thus exhibit mean reverting behavior. Fama and French (1988) and Poterba and Summers (1987) are among the first to provide direct empirical evidence that mean reversion occurs in US stock prices over long horizons. At the same time, other economists are critical of their results. Richardson and Stock (1989) and Richardson (1993) report that correcting for small sample bias may reverse the results found by Fama and French and Poterba and Summers mentioned above. Moreover, Kim et al. (1991) argue that mean reversion is a pre-World War II phenomenan and current stock prices exhibit mean averting behavior. The question of whether stock price-earnings contain transitory components poised in this paper is important for financial practice and theory. For example, consider technical analysis of stock price movements. If stock price-earnings ratios contain large transitory components, then observing a stock with a P/E ratio statistically far from its mean may establish a trend that could be traded technically. The notion of stock price trends is harshly rejected by many economists who argue in favor of the Efficient Market Hypothesis (EMH), which states that share prices reflect all information about a security, including information derived from fundamental and technical analysis. Therefore, it is theoretically impossible to consistently produce risk-adjusted excess returns, or alpha, and only inside information can result in outsized risk-adjusted returns. 2 5 This paper can also be used to evaluate the claims made by Keynes in his book The General Theory of Employment, Interest and Money (1936) where he states, “all sorts of considerations enter into market valuation which are in no way relevant to the prospective yield.” Poterba and Summers (1987) state that “if divergences between the market and fundamental value of a stock exist, but at beyond some limit are eliminated by speculative forces, then stock prices exhibit mean reversion.” Thus, if Keynes’ claim is true and the psychology of speculators can cause the market valuation of stocks to diverge from their fundamental values, evidence of mean reversion in P/E ratios should exist. Lastly, the results of this paper could have interesting implications on the Three-Factor- Model proposed by Fama and French (1992). To expand on the traditional Capital Asset Pricing Model (CAPM), Fama and French suggest stock returns are explained by size and valuation factors in addition to market risk. The valuation factor they employ is related to book-to-market value of a stock, which is highly correlated to the price-earnings ratio. If P/E ratios are mean reverting processes, there may be endogeneity in their valuation factor that is not properly accounted for. A more in-depth discussion of these implications is located in the Theory and Methodology section. This study fits in an extensively researched section of the financial literature but seeks to test for mean reverting behavior in stock price-earnings ratios rather than stock prices and utilizes a slightly different methodology than those used by economists such as Fama and French (1988). I utilize quarterly stock and sector data gathered from Bloomberg. The sample period ranges from 2008 to 2017. The outcome variable of interest is the distance of the current P/E ratio from its trailing five-year average and the explanatory variable of interest is its lagged value. This is a similar model used to test for mean reversion in stock prices by Balvers et al 3 6 (2000), but I introduce several more controls to achieve more accurate estimators. Moreover, much of the previous literature employs variance ratio tests and standard unit root tests for mean reversion. However, econometric studies by Campbell and Perron (1991), Cochran’s (1991) and DeJong et al. (1992) indicate that standard unit roots tests have very low power against local stationary alternatives in small samples. Further, Zhen (2010) argue that panel data can be used to generate more accurate unit root estimation. In this paper, I employ a linear regression model using panel data from S&P 500 companies to test for mean reverting processes in price-earnings ratios. While most of the previous literature examine stock price mean reversion, these results can be misleading. Stock price movements occur for a wide variety of reasons, many of which are either difficult or impossible to isolate. So, it will be difficult to isolate a reversion coefficient due to potential endogeneity from many unobserved variables. The price-earnings ratio of a company has well-grounded determinants, including expected growth, consistency of dividends, company size, and extent of analyst converge, to name a few. Including these variables as controls in a regression will allow me to get a more accurate and unbiased estimation of the presence of mean reverting behavior. The estimators of interest used in this paper are likely subject to several statistical biases due to the nature of the data. Issues that I found to be present through the use of rigorous econometric testing are heteroskedasticity, serial correlation and unit roots. The paper addresses them by employing heteroskedastic-robust standard errors while differencing and detrending each variable. There is also likely to be survivorship bias and small sample bias present in this analysis. I address the former by using both time-series panels and pooled panels but fail to address the latter due to limited time and resources. Regression results from both datasets 4 7 support the mean reverting hypothesis, showing evidence of mean reverting processes in US company price-earnings ratios from 2008-2017. The remainder of the paper is organized as follows. Section II will discuss the previous literature on stock mean reversion and the relationship between price-earnings ratios and stock returns. Section III will describe the theory behind my model and define the methodology used to achieve unbiased estimators of my coefficients. Further, Section IV will review the data used to address the research question. Finally, Section V will examine the results of the regression output and will be followed by a comprehensive conclusion for this paper. II. Literature Review Most of the existing literature relating to this topic simply employs unit root and stationarity tests to detect mean reversion in stock prices.
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